Influence of crystal structure on the lattice sites and formation energies of hydrogen in wurtzite and zinc-blende GaN

Charge-state calculations based on density-functional theory are used to study the formation energy of hydrogen in wurtzite and zinc-blende GaN as a function of Fermi level. Comparison of these results reveals notable differences including a 0.56 eV lower formation energy for ${\mathrm{H}}_2$ in wurtzite, and different configurations for ${\mathrm{H}}_2$ and ${\mathrm{H}}^{\mathrm{-}}$ in the two crystal structures. Furthermore, ${\mathrm{H}}^{+}$ is found to be equally stable at bond-centered and antibonding sites in wurtzite, whereas it is unstable at a bond-centered site in zinc blende. ${\mathrm{N}-\mathrm{H}}^{+}$ stretch-mode vibration frequencies, clustering of ${\mathrm{H}}^{+}$ in p-type material, and diffusion barriers for ${\mathrm{H}}^{\mathrm{-}}$ are investigated in wurtzite GaN. A diffusion barrier of 1.6 eV is found for ${\mathrm{H}}^{\mathrm{-}}$ in wurtzite GaN, significantly lower than a previous estimate, and a tendency for ${\mathrm{H}}^{+}$ clustering in p-type material is found.